Question

l and m are two parallel lines intersected by another pair of parallel lines p and q (see Fig. 7.19). Show that ∆ ABC ≅ ∆ CDA.

Answer 1

In ∆ABC and ∆CDA,

∠BAC = ∠DCA (Alternate interior angles, as p || q) 

AC = CA (Common)

∴ ∠BCA = ∠DAC (Alternate interior angles, as l || m) 

∴ ∠∆ABC ∆CDA (By ASA congruence rule)